Chapters II-V of Quantum Mechanics of
The Bible According to Einstein

All rights reserved. No part of this website may be reproduced or transmitted in any form or by any means, electronic or mechanical including photocopying and recording, or by any information storage and retrieval system without written permission from the publisher.

Copyright ©1999 by Jupiter Scientific Publishing Company


To the index of The Bible According to Einstein

(Adjust width of browser to the width of the running title (the first line). Much of the formatting of The Bible According to Einstein cannot be implemented in html)



To Chapter I back To Chapters VI-XIII next


212                       The Bible According to Einstein




Chapter II: Paths

Ask among all paths, which is the good way?
And walk therein, for ye shall find there peace.
Now quantum mechanics has two formulations. And the first is the path integral. Now the position of a moving particle as time evolves shall constitute the particle's trajectory. Thus a trajectory shall be a curve through space and time. And because it is a curve in space and time, it shall also be a path. And a point on the path at a particular time shall be the position of the particle.



The New Testament                                       213
      And it is as though thou walkest along a wooded valley trail between two mountains. And thou beginst thy walk at the beginning of the trail. And thirty minutes later, thou hast traversed one mile of track. And one hour later, thou art two miles from the start. And two hours later, thou finishest thy walk. And since thou traverst the trail in a steady manner, anyone knows where thou art at any time. Thy motion is predictable. And thy positions at various times constitute a known trajectory. Thus in this example, the trajectory is the trail itself.
      Now in classical mechanics, there shall be but one trajectory, or path. And this path shall be computable from Newton's laws. And it shall be called the classical trajectory. And knowledge of this path shall provide knowledge of the position of any object in the future, at the present, or in the past.
      In classical mechanics, it is as though thou be infinitely lazy. And choosest thou the path of least resistance. And avoidest thou steep mountain slopes, so that thou walkest along the center of the valley. And though thou be tempted to take a short cut, it involves climbing and descending. And thou mightest want to pass along a longer, perhaps-more-scenic route, but lazy as thou art, takest thou the easy path, the lazy path.

Only poets choose the path less travelled by.

      And for thee, the classical trajectory shall be the predictable, well-travelled trail. But in quantum mechanics, thou shalt be free. Thou shalt be allowed to walk along all paths.

Quantum mechanics -- it be the democratization
of dictatorial classical-mechanics laws.

      So in a quantum mechanical world, an object shall transverse all paths. But some paths shall be more preferable than others. And the most preferred path of all shall be the classical trajectory. And because all paths are included, it shall be impossible to predict with certainty where an object be at a given moment. Thus uncertainty shall be a property of quantum mechanics. And this effect shall have a name -- the uncertainty principle shall be its name.
      And suppose thou livest in a quantum world and thou beginst thy walk. Now in this quantum case, thou dost not plan thy walk. And thou art only somewhat lazy. So most of the time, movest thou along the local trail of least resistance. But sometimes, decidest thou to profit from a short cut. And sometimes, thou decidest to ascend a little hill. And sometimes, thou decidest to take a longer route. And these decisions are made randomly but preferably, because preferest thou the easy trails.


213                        The Bible According to Einstein
And friends who are waiting for thee will be frustrated and annoyed because they do not know where thou be for sure. And although it is most probable that thou art on or near thy favorite well-travelled trail, thou perhaps hast gone astray.
      And this formulation of quantum mechanics shall be called the path integral because "integral" means "to include all."

Chapter III: Quantum Mechanics, Philosophers,
Scientists and God
And philosophers will debate the meaning and implications of quantum mechanics and be particularly concerned about uncertainty. And many will be frustrated and annoyed. But, as for the uncertainty principle, scientists will understand it. And Nature simply shall obey it.

To decide and then revise. To decide and then retreat.
Uncertainty will certainly confuse the wise.

      And theorists using the rules of quantum mechanics will carry out countless computations. And the computations will all agree with countless experiments performed by experimentalists. And scientists will develop a great trust in quantum-mechanical dynamics. And for some scientists, the faith will be as strong as a Christian's faith in God.
      Now as a consequence of the uncertainty principle, it shall be impossible to know simultaneously and exactly the position and momentum of an object.195 Thus position and momentum in quantum mechanics shall only probabilistically be known. And this shall be completely different from the notion of position and momentum in classical mechanics, where they are known with certainty.

Chapter IV: The Planck Constant
and Quantum Hills
Now quantum mechanical behavior and uncertainty shall be controlled by a fundamental number. And this fundamental parameter shall have a name -- Planck's constant shall be called its name.
      And theorists will pretend that they can control Planck's constant. And if they play the game of "god" and set the constant to zero, then the classical and quantum worlds will coincide. And making Planck's constant smaller shall be like making the slopes of hills and mountains steeper. And so a somewhat lazy walker will be forced to walk quite near the trail of least resistance. And if the theorists do play "god" and make the constant zero, then they make the slopes of hills and mountains infinitely steep -- with giant hands they fold together mountains. And valleys turn into crevasses.

____________________

195 This effect becomes particularly important for microscopic objects, such as atoms and electons.




The New Testament                                       215
Walkers become completely trapped. And then even the most energetic motivated hiker is compelled to traverse the crack of least resistance. And since this crack is the classical trajectory, the motion shall be predictable and classical.
      But in the real world, Planck's constant is 6.6  x 10-34 Joule-seconds. Although miniscule, it is nonetheless not zero. And nobody, neither scientists, nor philosophers, nor holy men, nor theorists can make the constant zero. Such be written in firm stone. But since the constant is so small, classical mechanics shall often be a good approximation. And because the constant is so small, quantum mechanical effects shall only in the microscopic world be manifest at all. Thus atoms, nuclei, nucleons, electrons, quarks and other microscopic bodies shall feel quantum effects, but living bodies, blocks and balls shall not. And even in the microscopic world, the hills and valleys shall be very small.
      And ants may struggle to pass around a tiny pebble, rock or clump of dirt, but elephants do not.

And quantum mechanics shall govern all --
All shall hearken to its song.
And quantum mechanics shall dominate the small.

Chapter V: Tunnelling
And quantum tunnelling and barrier penetration shall be a consequence of the uncertainty of paths. In the quantum world, a marble in a coffee cup, in principle, may suddenly jump out. A path exists which climbs the cup and spout. And from the spout, quickly would the marble fall. But for this path, the probability is very very small. And during the lifetime of the Universe, the marble will not jiggle its way out.
      But in the subatomic world, a body has a better chance to climb a wall. And sometimes, like an army scout who leaves the troops and climbs a little hill, a particle will jump and manage to get out. How foreign from the world of man be the world of the quantum and the small. And if a microscopic particle should suddenly surmount a wall, one need not shout nor be alarmed -- this is what barrier penetration is about.
      Now a process, which proceeds along a quantum path through a classically forbidden region, shall by definition be quantum tunnelling or barrier penetration. And the decay of a radioactive nucleus shall take place by means of quantum penetration. Such a nucleus shall be like unto a marble in a cup.

Quantum mechanics shall be
full of fluctuations for objects of small size.
The quantum wings shall flap
like unto the wings of butterflies.





To Chapter I back To Chapters VI-XIII next



Copyright ©1999 by Jupiter Scientific Publishing Company

To the index of The Bible According to Einstein